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This is: A Model of Patient Spending and Movement Building, published by NunoSempere, trammell on the AI Alignment Forum.
This project began during Nuño's 2020 summer research fellowship at FHI. Phil was the project mentor.
Motivation
The EA movement has tradeoffs to make about where to deploy its capital and labor. However, for now, these decisions seem like they are mostly made heuristically and intuitively.
To make those decisions more robust, we have set up a reasonably general model to try to capture the most important dynamics. We hope that the model is informative enough to influence decisions directly, and that it motivates more gathering and systematization of empirical data about variables that the model finds crucial (rate of expropriation, the shape of returns to movement building, etc.). We also hope that it inspires further modelling work.
Setup
The model looks something like:
That is, the social movement has access to labor and capital.
In combination, they can be:
Allocated to paid movement-building efforts, which return more labor
Allocated to direct work, which returns goods in the world (malaria nets, etc.)
Alone, capital can be:
Transformed into more capital with time
Transformed into labor through hiring (only possible in one of the two models; this is why this step is greyed out in the diagram)
Alone, labor can be:
Left alone to produce more labor, or decay, depending on the specifics of the model
Allocated to earning to give, which returns more capital (only possible in one of the two models; this is why this step is grayed out in the diagram)
Note that the diagram only lays out the possible flows of labor and capital, but many parameters and functions determine how exactly that flow looks in practice. The paper defines these in more detail, but some which turn out to be important are:
Utility is isoelastic in "direct work", meaning that as the quantity of "direct work" (e.g., malaria nets delivered) increases, the utility function is assumed to have constant curvature, in a certain sense. For instance, as the number of malaria nets delivered increases, they get sent to places where the need for them is less great: this would imply a curvature that is less than linear. In our model, this curvature is represented by η. η = 1 defines a logarithmic utility function, η > 1 defines a function which exhibits sharper diminishing returns than the logarithm, and η < 1 defines a function that exhibits returns which diminish more slowly. (η = 0 defines linear utility.)
Diminishing returns under some values for η in a isoelastic utility function
Capital has a rate of return r
δ is the “discount rate” (more technically, the time preference), i.e. the rate of intrinsically caring less about the future (pure time preference) we have—if any—plus the annual rate at which we collectively face risks of expropriation, value drift, existential catastrophe, etc.
Labor, if left alone, depreciates (i.e., movement participants leave or die), at a rate d
Labor productivity grows at a rate γ, to reflect the growing labor productivity seen in the economy as a whole
Using these functions and parameters, we set up a system in terms of rather general functions for the production of direct work and recruitment. We then solve it to arrive at the optimal solution, either across all points in time (if we allow for both earning to give and hiring) or only asymptotically (if we don't.)
If you are familiar with what the terms "isoelastic" and "constant elasticity of substitution" mean, you might want to just read the document.
Main results
If the social movement is "patient" (in that δ < r − γη), then under some reasonable assumptions about diminishing returns to movement building (see this comment), our model finds that total labor (i.e., total movement size) approaches a constant value. T...
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